Phantomless calibration of CT scans for hip fracture risk prediction in silico: Comparison with phantom-based calibration

Finite element models built from quantitative computed tomography images rely on element-wise mapping of material properties starting from Hounsfield Units (HU), which can be converted into mineral densities upon calibration. While calibration is preferably carried out by scanning a phantom with known-density components, conducting phantom-based calibration may not always be possible. In such cases, a phantomless procedure, where the scanned subject’s tissues are used as a phantom, is an interesting alternative. The aim of this study was to compare a phantom-based and a phantomless calibration method on 41 postmenopausal women. The proposed phantomless calibration utilized air, adipose, and muscle tissues, with reference equivalent mineral density values of -797, -95, and 38 mg/cm3, extracted from a previously performed phantom-based calibration. A 9-slice volume of interest (VOI) centred between the femoral head and knee rotation centres was chosen. Reference HU values for air, adipose, and muscle tissues were extracted by identifying HU distribution peaks within the VOI, and patient-specific calibration was performed using linear regression. Comparison of FE models calibrated with the two methods showed average relative differences of 1.99% for Young’s modulus1.30% for tensile and 1.34% for compressive principal strains. Excellent correlations (R2 > 0.99) were identified for superficial maximum tensile and minimum compressive strains. Maximum normalised root mean square relative error (RMSRE) values settled at 4.02% for Young’s modulus, 2.99% for tensile, and 3.22% for compressive principal strains, respectively. The good agreement found between the two methods supports the adoption of the proposed methodology when phantomless calibration is needed.


Kernel distribution fitting procedure
Voxels in the ROI were used to build a histogram (bin width 1 HU), which was later fitted with a kernel distribution using a normal smoothing function with a 5 HU bandwidth (Fig S1).For that purpose, Matlab (release R2022b, The Mathworks Inc) built-in function fitdist was used.

Minimum Side-Fall Strength analysis
Relative error on Minimum Side-Fall Strength (MSF), i.e., the lowest load to failure across the 28 femoral impact poses between phantom-based and phantomless calibration method for each subject from Group 2 is shown in Table S3.

ARF0 analysis
The obtained values of ARF0 for each subject in Group 2 for both calibration methods, along with the absolute differences are shown in Table S4.

Prior analysis
While employing the method with the reference density values proposed in Eggermont et al. (2019), we obtained notable errors in Young's modulus, tensile (ε1) and compressive (ε3) principal strains shown in the Table S5.The table reports errors computed with respect to the phantom-based calibration in terms of both the root mean square relative error (RMSRE) and relative differences in Young's modulus, tensile (ε1) and compressive (ε3) principal strains for the 10 subjects belonging to Group 2 (S01-S10).

Fig S1 .
Fig S1.Example of histogram of ROI with fitted distribution for air (a) and adipose and muscle (b).The anomaly bin around HU = -1020 in subfigure (a) represents pixel values used in the image to pad to a rectangular format.These pixels are not part of the anatomical image.The smoothing bandwidth was determined through convergence analysis of the obtained HU peak values, aiming to achieve an error smaller than 5 % (FigS2).

Fig S2 .
Fig S2.Convergence analysis for different bandwidth values.Error was computed on obtained HU values for air, adipose and muscle tissue for each bandwidth to the values obtained for the lowest one.

Fig S3 .
Fig S3.Distribution of element-wise relative differences in Young's modulus between both calibration methods.Violin plots showing the distributions of element-wise relative differences in Young's modulus values between phantom-based and phantomless calibration for Group 2 subjects.The solid black line represents the mean value, while the blue solid line represents the median.

Fig S6 .
Fig S6.Spatial distribution of relative differences between Young's modulus values coming from the phantom-based and phantomless calibrations for S17.Frontal plane is the mean frontal section from the anterior view of the femur.

Fig S7 .
Fig S7.Average point-to-point relative differences (%) in superficial tensile strains between the phantom-based and phantomless methods.

Fig S9 .
Fig S9.Average point-to-point relative differences (%) in superficial compressive strains between the phantom-based and phantomless methods.

Fig S11 .
Fig S11.Distribution of point-to-point relative differences in superficial principal strains coming from both calibration methods.Violin plots showing the distributions of the point-to-point relative differences computed on superficial tensile (a) and compressive (b) principal strain values between phantom-based and phantomless calibrations, considering all 28 simulated femur impact poses for each the 17 subjects in Group 2. The solid black line represents the mean, the blue solid line represents the median.